Information on Result #1324004
Linear OA(4180, 65588, F4, 28) (dual of [65588, 65408, 29]-code), using construction X with Varšamov bound based on
- linear OA(4178, 65585, F4, 28) (dual of [65585, 65407, 29]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(49, 49, F4, 5) (dual of [49, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(4178, 65586, F4, 26) (dual of [65586, 65408, 27]-code), using Gilbert–Varšamov bound and bm = 4178 > Vbs−1(k−1) = 143076 122635 026415 045317 986283 148135 057485 943428 828728 444912 243764 398271 101606 416066 241569 141723 289601 367320 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4180, 32794, F4, 2, 28) (dual of [(32794, 2), 65408, 29]-NRT-code) | [i] | OOA Folding | |